Scalarization of dyadic spectral Green's functions and networkformalism for three-dimensional full-wave analysis of planar lines andantennas

A novel and systematic method is presented for the complete determination of dyadic spectral Green's functions directly from Maxwell's equations. With the use of generalized scalarizations developed in this paper, four general and concise expressions for the spectral Green's functions for one-dimensionally inhomogeneous multilayer structures, excited by three-dimensional electric and magnetic current sources, are given in terms of modal amplitudes together with appropriate explicit singular terms at the source region. It is shown that Maxwell's equations in spectral-domain can be reduced, by using dyadic spectral eigenfunctions, to two sets of z-dependent inhomogeneous transmission-line equations for the modal amplitudes. One set of the transmission-line equations are due to the transverse current sources and the other set due to the vertical current sources. Utilizing these equations, network schematizations of the excitation, transmission and reflection processes of three-dimensional electromagnetic waves in one-dimensionally inhomogeneous multilayer structures are achieved in a full-wave manner. The determination of the spectral Green's functions becomes so simple that it is accomplished by the investigation of voltages and currents on the derived equivalent circuits. Examples of singleand multilayer structures are used to validate the general expressions and the equivalent circuits     

Nodal-based finite-element modeling of Maxwell's equations

Weak forms are derived for Maxwell's equations which are suitable for implementation on conventional C⁰ elements with scalar bases. The governing equations are expressed in terms of general vector and scalar potentials for the electric field intensity vector. Gauge theory is invoked to close the system and dictates the continuity requirements for the potentials at material interfaces as well as the blend of boundary conditions at exterior boundaries. Two specific gauges are presented, both of which lead to Helmholtz weak forms which are parasite-free and enjoy simple, physically meaningful boundary conditions. A general and numerically efficient procedure for enforcing the jump discontinuities on the normal components of vector fields at dielectric interfaces and boundary conditions on curved surfaces is also given     

General solutions of Maxwell's equations for signals in a lossymedium. I. Electric and magnetic field strengths due to electricexponential ramp function excitation

Modification of Maxwell's equations to obtain general solutions for a lossy medium is reviewed. It is done by adding an extra term, referred to as the fictitious magnetic charge density. The solutions, which are in integral form, are solved numerically by computer for an exponential ramp function excitation. Computer plots for the electric and magnetic field strengths as functions of time at different locations in a lossy transmission medium are presented     

柱坐标系中阻抗劈表面的精确阻抗边界条件

本文首先给出一般阻抗面上的精确阻抗边界条件，然后把它应用到阻抗劈劈面上，结合麦克斯韦方程，考虑平面波相对阻抗劈边缘垂直入射和斜入射两种情况，导出了柱坐标系中阻抗劈表面以一阶偏微分方程形式表达的精确阻抗边界条件。     

General solutions of Maxwell's equations for signals in a lossymedium. III. Electric and magnetic field strengths due to electric andmagnetic sinusoidal pulse excitation

For pt.II see ibid., vol.30, no.1, p.37-40 (1988). The representation of a function with a general time variation by a series expansion of time-shifted transients is discussed. On the basis of this representation, numerical solutions of Maxwell's equations are presented for the electric and magnetic field strengths in a lossy medium due to electric and magnetic excitation functions consisting of a finite number of sinusoidal cycles. The solutions are derived by means of a time-series expansion of the available solutions for the electric and magnetic exponential ramp function excitations     

Wave propagation in nonlinear electromagnetic media

This brief tutorial review first discusses the physical origin of nonlinear electric and magnetic susceptibilities of electro-magnetic media, from the audio through the microwave to the visible range of the electromagnetic spectrum. Wave propagation in non-linear media can be described by a combination of Maxwell's equations and the nonlinear constitutive equations. The Manley-Rowe relationships are verified for anisotropic lossless dielectrica. Microwave harmonic generation in ferrites and other materials, microwave modulation of light, light harmonic generation, light mixing and parametric conversion are all discussed from a general common viewpoint. The boundary conditions at the surface of a nonlinear medium lead to generalizations of the laws of reflection and refraction of light.     

Scattering by an arbitrary cylinder at a plane interface: broadsideincidence

The problem of the determination of the fields scattered by an infinite dielectric cylinder of arbitrary cross section located at the interface between two semi-finite dielectric media is reduced to the solution of integral equations for unknown functions defined on the boundaries. These boundary functions are chosen so as to minimize their number. The incident field is that of a plane monochromatic wave. The derivation of the integral equations is given for the transverse electric (TE) mode for a dielectric cylinder and for a perfectly conducting cylinder. The exact electromagnetic fields are obtained from the solutions of the integral equations by integration, and the radar cross section can be computed from the far-field approximation. Sample outputs of the computer programs that implement this solution are shown     

Electromagnetic Waves in Toroidal Vessels of Arbitrary Cross Section Filled with Radially Inhomogeneous Dielectric Medium

In this paper, analytical solutions of Maxwell's equations in cylindrical coordinates are presented for toroidal resonators filled with homogeneous or inhomogeneous unmagnetized plasma or another dielectric medium. It is shown that the electromagnetic boundary conditions valid on a conducting toroidal surface of arbitrary meridional cross section can be satisfied by the general solution since the general solution contains an infinite set of arbitrary constants. A method is given to show how these constants and the eigenfrequency of the resonator can be calculated for a given cross section of the toroidal vessel.     

A failure of a numerical electromagnetics code to match a simpleboundary condition

It is shown that it is impossible to satisfy the boundary condition for a perfectly conducting hemisphere-capped dipole without creating a discontinuity in the first derivative of the scattered field on the boundary. Since solutions of Maxwell's equations are analytic in a source-free region, all field derivatives must be continuous in the region where the source-free equations are satisfied. The basis functions used by the generalized multipole technique (GMT) are solutions of Maxwell's source-free equations in a region which includes the scattering surface. Therefore, a GMT solution to the dipole problem can exist only in the sense that the boundary value error approaches zero as the number of basis functions approaches infinity. This in itself is not surprising, but the difficulty of matching the boundary condition at the discontinuity affects the convergence of the technique. For the method-of-moments (MOM) technique, where a source current exists on the scattering surface, it is not clear if a perfect boundary value solution to the dipole problem can be theoretically realized or not     

Application of Hill's functions to problems of propagation in stratified media

A novel method of solving Maxwell's equations in a plane-stratified dielectric layer is presented, The governing differential equations for each polarization are solved in terms of Hill's functions. The formulation yields solutions which are formally exact and applicable to an extremely wide range of dielectric variations within the layer, without restriction to any particular frequency regime. The method is used to study the reflection of a plane wave polarized parallel to the plane of incidence by an inhomogeneous layer separating two homogeneous regions of infinite extent. The effect of the graded boundary on the Brewster-angle phenomenon is discussed for the case where the two homogeneous regions have different dielectric properties. Reflections from a dielectric duct are also considered as an illustration of the utility of the method.     

A comparison of transient solutions of Maxwell's equations to thatof the modified Maxwell's equations

In 1986 H.F. Harmuth introduced a modification of Maxwell's equations to study the propagation of transient electric and magnetic field strengths in lossy media. Opponents of this modification of Maxwell's equations have claimed and attempted to demonstrate that Maxwell's equations in their known forms can correctly be solved, for example by the Laplace transformation method, to obtain solutions of transient electric and associated magnetic field strengths in lossy media without encountering any difficulties. This work presents detailed computer plots of Harmuth's transient solutions of the modified Maxwell's equations and that of Maxwell's equations solved by the Laplace transformation characteristic for the two solutions, which indicate that they are not the same. It is shown that Harmuth's procedure results in physically more plausible solutions     

非笛卡儿张量分析在计算电磁学中的应用

采用以非笛卡儿张量分析为基础的广义矩阵法，来推求任意曲线坐标系中计算电磁学的基本方程－Ｍａｘｗｅｌｌ方程，从而根据物理问题的边界几何形状，可以简便地导出选用的三维空间任意曲线坐标系中的解析式。本文提出了Ｍａｘｗｅｌｌ方程组基本的，适用于任意坐标系的张量公式及广义矩阵公式，还揭示了推求正交或非正交的曲线坐标系中Ｍａｘｗｅｌｌ方程组的示例。该法还可推广到求四维场的表达式等诸方面。     

Physical wavelets and radar: a variational approach to remotesensing

Physical wavelets are acoustic or electromagnetic waves, resulting from the emission of a time signal by a localized acoustic or electromagnetic source moving along an arbitrary trajectory in space. Thus, they are localized solutions of the wave equation or Maxwell's equations. Under suitable conditions, such wavelets can be used as “basis” functions, to construct general acoustic or electromagnetic waves. This gives a local alternative to the construction of such waves in terms of (nonlocal) plane waves, via Fourier transforms. We give a brief, self-contained introduction to physical wavelets, and apply them to remote sensing. We define the ambiguity functional, generalization of the radar and sonar ambiguity functions, which applies not only to wideband signals, but also to targets and radar platforms executing arbitrary nonlinear motions     

Nonsinusoidal Waves in Cavity Resonators

It has been shown that nonsinusoidal waves can propagate dispersion-free in loss-free waveguides. This situation opens the possibility of nonsinusoidal waves existing distortion-free in cavity resonators. A general solution of Maxwell's equations for nonsinusoidal waves in rectangular cavity resonators is derived. For the special case of a square wave, the electric and magnetic field strengths as functions of time and space are analyzed in detail. The implication of this analysis is that square waves or other periodic nonsinusoidal waves with various periods T can be separated by cavity resonators just as sinusoidal waves with various periods T can be separated. This paper is part of an ongoing effort to advance the technology of antennas and associated circuits for nonsinusoidal electromagnetic waves.     

Electromagnetic fields in the presence of rotating bodies

Field calculations in the presence of rotating bodies with symmetry of revolution can be performed in the (inertial) laboratory frame of reference. Specific results are presented for a rotating circular cylinder immersed in a plane wave of the E or H type. Particular emphasis is put on the low-frequency limit, but some numerical data are also given for a typical frequency in the "resonance" region. The analysis becomes more complicated in the absence of symmetry of revolution. It is then necessary to solve the problem in a rotating system of coordinates. Maxwell's equations are written in these coordinates, together with the relevant constitutive equations and boundary conditions. The general formalism is applied to a typical two-dimensional configuration, viz., a cylinder immersed in an incident E wave. Considerable simplification obtains if all material velocities are negligible with respect to c, a condition which is always met in practice. Even simpler results are obtained if the cross-sectional dimensions of the cylinder are small with respect to λ. Some numerical results are presented, at low frequencies, for a dielectric cylinder of rectangular cross section.     

Guided Waves in Inhomogeneous Focusing Media Part I: Formulation, Solution for Quadratic Inhomogeneity

This work is a theoretical study of waves in a circular-cylindrical radially inhomogeneous guiding medium. A vector theory based upon Maxwell's equatious is used to derive linear homogeneous fourth-order equations satisfied by the longitudinal electric and magnetic field components for a medium in which the permittivity decreases monotonically from the propagation axis. The percentage change of permittivity from the guide axis to some radius a is assumed small. For modes with propagation constants approximately equal to the wave number at guide center, all field components are shown to satisfy second-order differential equations. In particular, all transverse field components are proportional to a single scalar function. In a Iossless system with no containing boundary, a new class of polynomial-Gaussian solutions describes the longitudinal fields for the case of a quadratically decreasing permittivity, while the transverse fields are Gaussian-Laguerre. Mode patterns, propagation constants, and orthogonality relations are given. It is shown analytically that the modes tend to TE or TM as the mode order increases. Moreover, the transverse fields become dominant at large wave numbers, and the fields become tightly bound to the guide axis as the wave number and/or inhomogeneity increases. Studies of more general permittivity variations and wall effects will be reported shortly.     

General Solution for Excitation by Slotted Aperture Source in Conducting Cylinder with Concentric Layering

We present a general matrix analysis for the electromagnetic fields produced by an aperture source on the inner metallic snrface of a concentrically layered structure. Each layer is homogeneous and characterized by arbitrary permittivity, conductivity and magnetic permeability. The structure itself is assumed to be of infinite length so Maxwell's equations yield separable solutions. An explicit result is given for the electric current density on the inner metallic cylindrical surface which could model the mandrel in a borehole logging tool.     

Diffraction of guided waves by the end face of a dielectric slab waveguide terminated with a finite conductive strip

The diffraction of guided waves by the end face of a dielectric slab waveguide short circuited with a finite conductive strip is analyzed. An integral equation technique is employed to formulate the corresponding boundary problem. The unknown term in this integral equations is the electric field E(x) on the terminal plane of the waveguide. The homogeneous term is determined from the incident guided wave. A method of moments technique is employed to compute approximately the electric field E(x) by using Laguerre functions as describing and testing functions. The reflection coefficients of the guided waves are computed by using the approximate expression of the E(x) field. Numerical results are given for several guide and conductor plate dimensions.     

Propagation of transients in dispersive dielectric media

The propagation of transient electromagnetic fields in dispersive dielectric media is studied. The dielectric medium is assumed to be linear, isotropic, and homogeneous, and is described by the Debye model. Incident fields are assumed to be transverse electromagnetic plane wave pulses. The dielectric body can assume the form of infinite half space or an infinite circular cylinder, either of which may be homogeneous or stratified. The electric fields induced in the dielectric are calculated from time-domain Maxwell's equations using the finite-difference time-domain method.<>     

The Maxwell's equations in the sense of distributions

It is well known that there is no direct one-to-one correspondence between the electromagnetic theory based on the physical laws and that based on the Maxwell's differential equations. For example, in order to derive the boundary conditions from the Maxwell's differential equations, one assumes that some integral identities derived from them are valid even when the field components (or material parameters) are discontinuous. This assumption violates, in a sense, the completeness of the theory of electromagnetism based on the Maxwell's differential equations. We will prove that if one postulates that the Maxwell's equations are valid in the sense of distributions, then this incompleteness will be removed and the boundary conditions will appear implicitly in the basic differential equations.